`\text{a) gọi ƯCLN( 3n + 2 ; 5n + 3 ) = d , ta có}`
\(\left\{\begin{matrix}3n+2⋮d\\5n+3⋮d\end{matrix}\right.\Rightarrow\left\{\begin{matrix}5\left(3n+2\right)⋮d\\3\left(5n+3\right)⋮d\end{matrix}\right.\)
\(\Rightarrow5\left(3n+2\right)-3\left(5n+3\right)⋮d\)
\(\Rightarrow15n+10-15n-9⋮d\)
\(\Rightarrow15n-15n+10-9⋮d\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
\(\text{Vậy phân số \(\dfrac{3n+2}{5n+3}\) là phân số tối giản (Đpcm)}\)
`A=6/15.18+6/18.21+6/21.24+...+6/87.90`
`A=2(3/15.18+3/18.21+3/21.24+...+3/87.90)`
`A=2(1/15+1/18-1/18+1/21-1/21+1/24-1/24+...+1/87-1/90)`
`A=2(1/15-1/90)`
`A=2. 1/18`
`A=1/9`
